Motion of bubbles towards the boundary for the Cahn–Hilliard equation

In this work we describe some aspects of the dynamics of the Cahn–Hilliard equation. In particular, we consider the dynamics of ‘bubble’ solutions that is spherical interfaces which move superslowly towards the boundary without changing their shape. We show for the Cahn–Hilliard that the bubble drifts towards the closest point on the boundary provided it is sufficiently small. This is contrasted with the related mass conserving Allen–Cahn equation where size is not an issue.